Question

Prove: m∠PTQ=m∠RTS. By the Nine geometry isn't fun. thanks

Answer 1

The image shows the diagram and the table of the proof. The proof is based on using the properties of equality and angles to show that m∠PTQ and m∠RTS are equal. Here are the steps and reasons in a code block:

Prove: m∠PTQ = m∠RTS

Steps | Reasons

Angles forming a linear pair sum to 180 | Definition of Supplementary Angles

m∠QTR + m∠RTS = 180 | Angles forming a linear pair

m∠PTQ + m∠QTR = 180 | Angles forming a linear pair

m∠QTR + m∠RTS = m∠PTQ + m∠QTR | Reflexive Property of Equality

m∠RTS = m∠PTQ + m∠QTR - m∠QTR | Subtraction Property of Equality

m∠RTS = m∠PTQ | Substitution Property of Equality

Explanation: